The Problem: R

library(tidyverse)

# Create a grid of points
x <- seq(-10, 10, by = 1)
y <- seq(-10, 10, by = 1)

# Prepare Data
grid <-
  expand_grid(x = x, y = y) |> 
  mutate(u = -y, v = x) |> 
  mutate(norm = sqrt(x^2 + y^2)) |> 
  mutate(u = u/max(norm), v = v/max(norm))

# Plot the vector field
ggplot(grid, aes(x = x, y = y)) +
  geom_segment(
    aes(xend = x + u, yend = y + v), 
    arrow = arrow(length = unit(0.1, "cm"))
    ) +
  theme_minimal() +
  labs(title = "Vector Field of f(x,y) = (-y, x)", 
       x = "X", y = "Y"
       )

The Problem: R

• This is verbose
  
• This is clunky
  
• This requires a lot of burden on the user

Current Solutions: Python

import numpy as np
import matplotlib.pyplot as plt

# Create a grid of points
x = np.linspace(-10, 10, 20)
y = np.linspace(-10, 10, 20)
X, Y = np.meshgrid(x, y)

# Define the vector field
U = -Y
V = X

# Plot the vector field
plt.quiver(X, Y, U, V)
plt.title("Vector Field")
plt.xlabel("X")
plt.ylabel("Y")
plt.show()

Current Solutions: Mathematica

xRange = Range[-10, 10, 1];
yRange = Range[-10, 10, 1];
grid = Flatten[Table[{x, y}, {x, xRange}, {y, yRange}], 1];

(* Define the vector field *)
vectorField = Table[{x, y, -y, x}, {x, xRange}, {y, yRange}];
vectorField = Flatten[vectorField, 1];

(* Plot the vector field *)
VectorPlot[{ -y, x }, {x, -10, 10}, {y, -10, 10}, 
 VectorPoints -> Fine, VectorScale -> Small,
 AxesLabel -> {"X", "Y"},
 PlotLabel -> "Vector Field of f(x,y) = (-y, x)"]

Proposed Solutions: ggvfields

• Introduction of the ggvfields package
• show github

geom_vector_field

• show base code to do this
• show a lot of reasonable variations
• future work

geom_streamplot

• show base code to do this
• show a lot of reasonable variations
• future work

geom_complex_function

• show base code to do this
• show a lot of reasonable variations
• future work

• should i show inner code?
• do i need to show how ggplot2 layers work?
• how much variation do i need to do on all the options?
• should i show how each of these functions work in other languages

The Problem:

Imagine one of several scenarios
- Researcher who desires to replicate another’s research
- Researcher who wants to use an previous study’s results as a prior for their own

Current Solutions

By hand

• slow
• error prone

mtcars |> 
  ggplot(aes(hp, mpg)) +
  geom_point()

Current Solutions

• email authors
• many reasons why this could go wrong
• such as unwilling/unable to share data

Current Solutions

plotdigitizer
automeris.io
engegue-digitizer
(show images of this)

• Problems: require user interaction, technical expertise, not 100% accurate

ChatGPT

• Problems: cost money, not 100% accurate, different answers every time asked

Proposed Solution

1. Neural Network Solution

2. Methodology

   • All Assumptions made in first model
   • Data Generation
   • AWS implementation (details)

3. Challenges

   • Money
   • Time
   • Size of neural network

4. Preliminary results with assumptions

5. Preliminary results by removing assumptions

6. Current unsolved issues

   • Unlimited y axis
   • Learn y axis?

7. Where to go from here